Find temperature change required

[utkarshakash]

Homework Statement

A smooth vertical tube having two different sections is open from both ends equipped with two pistons of different areas figure. Each piston slides within a respective tube section. One mole of ideal gas is enclosed between the pistons tied with a nonstretchable thread. The cross-sectional area of the upper piston is ΔS greater than that of the lower one. The combined mass of the two pistons is equal to m. The outside air pressure is P0. By how many Kelvin’s must the gas between the pistons be heated to shift the pistons through l?

Homework Equations

http://www.luiseduardo.com.br/mechanics/liquids/liquidsproblems_arquivos/image028.jpg

The Attempt at a Solution

Pressure of gas present inside = P₀ + mg/ΔS

I have a doubt regarding the pressure of the gas. Will it remain the same throughout the expansion? If yes, why?

 

[mfb]

You don't have to worry about the expansion process, it is sufficient to consider the situation in equilibrium - and there, your formula is valid independent of the expansion that happened.

 

[utkarshakash]

You don't have to worry about the expansion process, it is sufficient to consider the situation in equilibrium - and there, your formula is valid independent of the expansion that happened.

What if the two pistons were connected by an ideal spring?

 

[SammyS]

Homework Statement

A smooth vertical tube having two different sections is open from both ends equipped with two pistons of different areas figure. Each piston slides within a respective tube section. One mole of ideal gas is enclosed between the pistons tied with a nonstretchable thread. The cross-sectional area of the upper piston is ΔS greater than that of the lower one. The combined mass of the two pistons is equal to m. The outside air pressure is P0. By how many Kelvin’s must the gas between the pistons be heated to shift the pistons through l?

Homework Equations

http://www.luiseduardo.com.br/mechanics/liquids/liquidsproblems_arquivos/image028.jpg

The Attempt at a Solution

Pressure of gas present inside = P₀ + mg/ΔS

I have a doubt regarding the pressure of the gas. Will it remain the same throughout the expansion? If yes, why?

That seems like a reasonable concern to have.

What pressure is required for this system to remain at a given level ?

 

[utkarshakash]

That seems like a reasonable concern to have.

What pressure is required for this system to remain at a given level ?

Since the process is quasi-static, the pressure inside must remain same at all times. Am I correct?

 

[SammyS]

Since the process is quasi-static, the pressure inside must remain same at all times. Am I correct?

I didn't notice the equation:

Pressure of gas present inside = P₀ + mg/ΔS​

.

That pretty much says that the pressure is the same after pistons move.

 

[mfb]

What if the two pistons were connected by an ideal spring?

Then you have a completely different problem.

 

[utkarshakash]

The answer is

$ΔT = \left( ΔP + \frac{mg}{ΔS} \right) ΔS l$